Question

1. Two types of customers make up the market for Armoyas. There are 100 type A customers, each of whom is willing to pay up to $10 for an Armoya. There are 50 type B customers, each willing to pay up to $8 for an Armoya. No customer wishes to buy more than a single Armoya. The monopolist cannot differentiate between the types of customer. The average and marginal cost of production is constant at $6/Armoya.

a)What is the selling price of the good, and how much profit does the monopolist make?

b) The monopolist is offered the opportunity to advertise Armoyas at a cost of $80. The advertisement is predicted to attract another 100 type B customers. Will the advertisement be placed? What is the selling price of the good, and how much profit does the monopolist make?

c) Suppose the advertisement attracts no new customers, but raises the price all existing customers are willing to pay by $1. Will the advertisement be placed? What is the selling price of the good, and how much profit does the monopolist make?

Answer 1

a) No. of type A consumers =100

No of Type B consumers = 50

Price paid by Type A consumers = $10

Price paid by Type B consumers = $ 8

To find selling price we need mark-up value which is not given in the question. So we assume the selling price as the average price of two = ($10+$8)/2 = $9

Therefore, Total Revenue from sale to two types of consumers = (100 x 10) + (50 x 8) = $1000 + $400 = $1400

Marginal cost of production = $6

Since each consumer consumes only one unit,

So, No of Amoya produced for type A goods = 100

No of Amoya produced for type B goods = 50

Total Production = 100+50 = 150 Amoya

therefore, total cost = 150 x $6 = $ 900

therefore, Profit made by the monopolist = total revenue - total cost = $ 1400 - $ 900 =$ 500

b) Advertisement cost = $ 80

Since, the advertisement is predicted to attract another 100 type B customers,

No of Type B consumers post advertisement = 50 + 100 = 150

Due to the increased no of type B consumers, the sale increases by 100 x $ 8 = $800

Since the earning of the monopolist (i.e., $800) is greater than the cost of advertisement (i.e., $80), the monopolist will invest in advertisement and it will be placed.

Selling Price = ($10+$8)/2 = $9

Total Revenue = (100 x $ 10) + (150 x $ 8) = $1000 + $1200 =$ 2200

Profit of the monopolist = Total Revenue - Total cost - Advertisement Cost = $2200 - $900 - $80 = $ 1220

c) Since no new customers are attracted to the market because of the advertisement, the number of type A and type B consumers remain same at 100 and 50 respecively.

This also raises the prices by $1

So now, Price paid by Type A consumers = $11

Price paid by Type B consumers = $9

Total revenue = (100 x $11) +(50 x $9) = $1100 + $450 = $1550

So by spending $80 on advertisement, the monopolist is now earning more by $150(as compared to case a,i.e., the original situation).

Thus the advertisement will be placed.

Selling Price of the good = ($11+ $9)/2 = $ 10

Total cost = (150 x $6) = $900 + $80 = $980

Now, profit = Total revenue - total cost = $1550 - $980 = $570